Constrained Community Detection in Social Networks

Abstract

Community detection in networks is the process by which unusually well-connected sub-networks are identified–a central component of many applied network analyses. The paradigm of modularity quality function optimization stipulates a partition of the network’s vertexes that maximizes the difference between the fraction of edges within communities and the corresponding expected fraction if edges were randomly allocated among all vertex pairs while conserving the degree distribution. The modularity quality function incorporates exclusively the network’s topology and has been extensively studied whereas the integration of constraints or external information on community composition has largely remained unexplored. We define a greedy, recursive-backtracking search procedure to identify the constitution of high-quality network communities that satisfy the global constraint that each community be comprised of at least one vertex among a set of so-called special vertexes and apply our methodology to identifying health care communities (HCCs) within a network of hospitals such that each HCC consists of at least one hospital wherein at least a minimum number of cardiac defibrillator surgeries were performed. This restriction permits meaningful comparisons in cardiac care among the resulting health care communities by standardizing the distribution of cardiac care across the hospital network.